Abstract
In this article we describe student flows through entry level mathematics courses at a large, urban, Hispanic-serving R1.Student course taking patterns at a large university are complicated and driven by a number of underlying factors. The declared major of a student tends to determine their basic course requirements, and the mathematics progression will follow the ultimate course need for that major. In turn, the ultimate course will fall into a number of typical groups that can be summarized as
Group | Course Goal |
|---|---|
STEM Intending - Science | MAC 2311/2281 Calculus I (C1) |
STEM Intending - Engineering | MAC 2312/2282 Calculus II (C2) |
STEM Intending - Mathematics or Computational Focus | MAC 2313/2283 Calculus III (C3) or higher |
Business Related | MAC 1105 College Algebra (CA) or MAC 2233 Business Calculus (BC) |
Health Science | MAC 1105 College Algebra (CA), MAC 1147 Precalculus (PC), or MAC 2311 Calculus (C1) |
Non-STEM Intending | MGF 1106 Social Choice Math (SM) or MGF 1107 Finite Math (FM) |
Here we analyze the course flows for the STEM Intending, Health Science and Business Related groups. These students typically enter college at either the College Algebra (CA), Precalculus (PC) or Calculus I (C1) levels and progress to some level that is dependent on their specific major.
In an effort to understand some aspects of student course taking behavior, we collected data from the institutional records for students taking College Algebra (CA) MAC 1105, Precalculus College Algebra (PCA) MAC 1140, Precalculus with Trigonometry (PC) MAC 1147, MAC 1114 (TR) Trigonometry, Business Calculus (MAC 2233), Calculus I (C1, including both MAC 2311 Calculus I and MAC 2281 Engineering Calculus I), Calculus II (C2, including both MAC 2312 Calculus II and MAC 2282 Engineering Calculus II), and Calculus III (C3, including both MAC 2313 Calculus III and MAC 2283 Engineering Calculus III). Over the ten year period from Fall 2013 to Summer 2024 we observe 143172 instances of course taking (possibly with repetition) within these courses among students from Fall 2013 to Summer 2024. This total corresponds to 71654 distinct students enrolling over this time period. Subgrouping by course and then splitting the groups into two five-year time periods from Fall 2013 to Summer 2018 and Fall 2018 to Summer 2024, inclusive, the enrollments are as shown in the following table.
Fall 2013 to Summer 2018 | Fall 2018 to Summer 2024 | |||||
|---|---|---|---|---|---|---|
Course | # | # Succeed | % Succeed | # | # Succeed | % Succeed |
Social Choice Math | 7,128 | 4,528 | 63.5 | 3,465 | 2,445 | 70.6 |
Finite Math | 5,906 | 4,047 | 68.5 | 5,104 | 4,052 | 79.4 |
College Algebra (1105) | 10,248 | 6,730 | 65.7 | 18,504 | 12,335 | 66.7 |
Precalculus College Algebra (1140) | 12,418 | 6,366 | 51.3 | 1,267 | 782 | 61.7 |
Precalculus with Trig (1147) | 3,220 | 1,887 | 58.6 | 9,817 | 7,045 | 71.8 |
Trigonometry (1114) | 6,925 | 3,575 | 51.6 | 1,286 | 849 | 66.0 |
Business Calculus | 5,926 | 3,356 | 56.6 | 8,844 | 6,687 | 75.6 |
Eng Calculus 1 | 820 | 614 | 74.9 | |||
Eng Calculus 2 | 1,362 | 971 | 71.3 | |||
Eng Calculus 3 | 845 | 681 | 80.6 | |||
Calculus 1 | 9,560 | 5,298 | 55.4 | 10,124 | 7,200 | 71.1 |
Calculus 2 | 6,691 | 3,703 | 55.3 | 6,325 | 4,509 | 71.3 |
Calculus 3 | 4,045 | 2,490 | 61.6 | 3,342 | 2,326 | 69.6 |
Total | 72,067 | 41,980 | 58.3 | 71,105 | 50,496 | 71.0 |
Using this data, we then collected the unique student instances in each course (without repetition), and combined them by student to create the course taking pattern of the student. In what follows, we give the number of students in each course followed by the number of those students who took the next course from CA to C3. We computed two statistics from this process.
First, we calculuated the percentage of students from a given source course (such as CA) found in a given target course (such as C1). This number is computed as
\[\begin{equation*} \frac{\#(\text{students who passed the source course (A/B/C) and attempted the target course})}{\#(\text{students who took the source course})} \end{equation*}\]
We then computed the percentage of students in the target course that came from the source course. This number is computed as
\[\begin{equation*} \frac{\#(\text{students who passed the source course (A/B/C) and attempted the target course})}{\#(\text{students who took the target course})} \end{equation*}\]
Note that in general, the second number is larger than the first since the denominator is smaller.
From Fall 2013 to 2018 we can visualize the course taking patterns of unique student instances as shown below.
The plot data is summarized below in the following table.
Source | PCA 1140 | TR 1114 | PC 1147 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 8319 | 1612 | 19.4 | 31.5 | 3300 | 39.7 | 36.5 | 1181 | 14.2 | 44.8 |
1114 | 5113 | 2238 | 43.8 | 24.8 | 151 | 3 | 5.7 | |||
1140 | 9042 | 202 | 2.2 | 7.7 | ||||||
Total in Target Course | 5113 | 9042 | 2634 | |||||||
Source | BC | C1 | C2 | C3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 8319 | 1771 | 21.3 | 40.8 | 1444 | 17.4 | 21.1 | 631 | 7.6 | 13.4 | 271 | 3.3 | 9.7 |
1114 | 5113 | 163 | 3.2 | 3.8 | 1949 | 38.1 | 28.5 | 938 | 18.3 | 19.9 | 461 | 9 | 16.5 |
1140 | 9042 | 2472 | 27.3 | 56.9 | 2160 | 23.9 | 31.6 | 976 | 10.8 | 20.7 | 466 | 5.2 | 16.6 |
1147 | 2634 | 126 | 4.8 | 2.9 | 1352 | 51.3 | 19.8 | 652 | 24.8 | 13.8 | 261 | 9.9 | 9.3 |
2233 | 4341 | 120 | 2.8 | 1.8 | 46 | 1.1 | 1 | 22 | 0.5 | 0.8 | |||
2311 | 6844 | 2846 | 41.6 | 60.2 | 1320 | 19.3 | 47.1 | ||||||
2312 | 4724 | 1889 | 40 | 67.4 | |||||||||
Total in Target Course | 4341 | 6844 | 4724 | 2802 | |||||||||
Similarly, the data from Fall 2018 to Summer 2024 is shown below.
and the data for this collected in the following tables.
Source | PCA 1140 | TR 1114 | PC 1147 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 15358 | 238 | 1.5 | 22 | 298 | 1.9 | 29.5 | 4018 | 26.2 | 47.5 |
1114 | 1084 | 259 | 23.9 | 25.7 | 41 | 3.8 | 0.5 | |||
1140 | 1009 | 56 | 5.6 | 0.7 | ||||||
Total in Target Course | 1084 | 1009 | 8451 | |||||||
Source | BC | C1 | C2 | C3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 15358 | 2891 | 18.8 | 37.2 | 1864 | 12.1 | 20.8 | 751 | 4.9 | 12 | 288 | 1.9 | 8.6 |
1114 | 1084 | 18 | 1.7 | 0.2 | 295 | 27.2 | 3.3 | 105 | 9.7 | 1.7 | 41 | 3.8 | 1.2 |
1140 | 1009 | 40 | 4 | 0.5 | 227 | 22.5 | 2.5 | 75 | 7.4 | 1.2 | 28 | 2.8 | 0.8 |
1147 | 8451 | 195 | 2.3 | 2.5 | 3597 | 42.6 | 40.1 | 1329 | 15.7 | 21.2 | 481 | 5.7 | 14.4 |
2233 | 7766 | 144 | 1.9 | 1.6 | 44 | 0.6 | 0.7 | 19 | 0.2 | 0.6 | |||
2311 | 8981 | 3460 | 38.5 | 55.2 | 1156 | 12.9 | 34.5 | ||||||
2312 | 6268 | 2131 | 34 | 63.6 | |||||||||
Total in Target Course | 7766 | 8981 | 6268 | 3351 | |||||||||
We can also compile the data allowing for student repetition of courses. That is, we aggregate the attempts for a source course counting each attempt made by a student, and then consider whether or not that student attempts a target course some number of times and count each instance there as well.
From the Fall of 2018 to Summer 2024 is shown below.
and the data for this collected in the following tables.
Source | PCA 1140 | TR 1114 | PC 1147 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 10327 | 1879 | 18.2 | 28 | 3829 | 37.1 | 31.4 | 1400 | 13.6 | 44.2 |
1114 | 6700 | 2886 | 43.1 | 23.6 | 209 | 3.1 | 6.6 | |||
1140 | 12211 | 287 | 2.4 | 9.1 | ||||||
Total in Target Course | 6700 | 12211 | 3169 | |||||||
Source | BC | C1 | C2 | C3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 10327 | 2081 | 20.2 | 35.4 | 1616 | 15.6 | 17 | 703 | 6.8 | 10.6 | 297 | 2.9 | 7.5 |
1114 | 6700 | 200 | 3 | 3.4 | 2499 | 37.3 | 26.4 | 1143 | 17.1 | 17.2 | 564 | 8.4 | 14.2 |
1140 | 12211 | 3306 | 27.1 | 56.3 | 2689 | 22 | 28.4 | 1181 | 9.7 | 17.7 | 558 | 4.6 | 14 |
1147 | 3169 | 159 | 5 | 2.7 | 1592 | 50.2 | 16.8 | 747 | 23.6 | 11.2 | 299 | 9.4 | 7.5 |
2233 | 5871 | 147 | 2.5 | 1.6 | 50 | 0.9 | 0.8 | 24 | 0.4 | 0.6 | |||
2311 | 9481 | 3701 | 39 | 55.6 | 1711 | 18 | 43.1 | ||||||
2312 | 6656 | 2659 | 39.9 | 66.9 | |||||||||
Total in Target Course | 5871 | 9481 | 6656 | 3974 | |||||||||
From the Fall of 2018 to Summer 2024 is shown below.
and the data for this collected in the following tables.
Source | PCA 1140 | TR 1114 | PC 1147 | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 18375 | 264 | 1.4 | 22 | 347 | 1.9 | 31.3 | 4419 | 24 | 44.8 |
1114 | 1201 | 303 | 25.2 | 27.3 | 43 | 3.6 | 0.4 | |||
1140 | 1109 | 62 | 5.6 | 0.6 | ||||||
Total in Target Course | 1201 | 1109 | 9859 | |||||||
Source | BC | C1 | C2 | C3 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
# | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | # | % from Src | % of Tgt | |
1105 | 18375 | 3203 | 17.4 | 36.6 | 1968 | 10.7 | 18.4 | 780 | 4.2 | 10.4 | 293 | 1.6 | 7.2 |
1114 | 1201 | 20 | 1.7 | 0.2 | 328 | 27.3 | 3.1 | 114 | 9.5 | 1.5 | 43 | 3.6 | 1.1 |
1140 | 1109 | 41 | 3.7 | 0.5 | 240 | 21.6 | 2.2 | 77 | 6.9 | 1 | 30 | 2.7 | 0.7 |
1147 | 9859 | 215 | 2.2 | 2.5 | 3982 | 40.4 | 37.3 | 1418 | 14.4 | 18.9 | 503 | 5.1 | 12.4 |
2233 | 8762 | 152 | 1.7 | 1.4 | 44 | 0.5 | 0.6 | 19 | 0.2 | 0.5 | |||
2311 | 10686 | 3796 | 35.5 | 50.6 | 1249 | 11.7 | 30.8 | ||||||
2312 | 7497 | 2486 | 33.2 | 61.2 | |||||||||
Total in Target Course | 8762 | 10686 | 7497 | 4059 | |||||||||